Packed beds have been utilized for various heat and mass transfer operations, e.g. adsorption, thermal storage, chromatography etc. The performance of packed beds in most of these systems is analyzed using concentration or temperature profile in the bed and their progression in time. It is desirable, in many systems, to have a profile which progresses in the form of sharp front. For such a profile, the space or material utilization is maximum and recovery is very efficient. However, many difficulties are encountered in real life to achieve such sharp front. In thermal or heat storage processes, having a profile with a sharp front becomes even more important due to exergetic efficiency. Shinnar has described certain ways to achieve this sharpness for thermal wave front. However, many systems, it is not feasible to obtain a sharp front. The relative steepness of the front can be increased by increasing the length of the bed traversed or connecting many such beds in series. But this method will largely increase the pressure drop incurred which will increase the operating costs, particularly for the case of gases as the carrier medium.
In any mass transfer or heat transfer operation involving surface or bulk absorption over packed beds, there is always an optimization between pressure drops incurred and transfer effectiveness. This optimization becomes significantly important if the fluids involved are gases as it is more expensive to compress gases. The adsorption, ion-exchange or absorption phenomena in packed bed are dependent upon on several factors such as fluid flow rates, mass transfer coefficient, packing shape and size, porosity etc. The effectiveness of the transport process over the bed is evaluated by the concentration profile of the solute. These concentration profiles, also known as breakthrough curves, determine the effectiveness by the steepness of concentration gradient spread over the bed. Higher steepness makes the system more effective and thus economically feasible. The additional savings for this system is reduction in compression costs considerably.
FIG. 1 depicts a moving adsorption front with constant thickness. Additional length of the bed represents higher fractional utilization. FIG. 1 exemplifies the progression of solute concentration front and illustrates that in order to completely saturate the original bed length it is necessary to introduce additional length (20% extra). The extra bed length implies additional pressure drop. Therefore, if fractional utilization is increased, compression costs increase as well. In case of very sharp fronts without any dispersion effects, such problems do not exist. However for not so sharp fronts and high pressure drop systems this design of a regular packed bed arrangement is not optimal. In fact for some applications such as flue gas treatment, higher pressure drops are not allowed so the overall fractional utilization is increased and systems become expensive.
There is a need for methods for optimizing the process of heat and mass transfer operations in packed beds. There is also a need for the application of those methods for optimizing the process.